A 1300kg car going 20m/s has to stop suddenly. The driver locks the brakes, and the car skids to a halt in a distance of 64m .
What was the car's acceleration while stopping?
How much work was done by friction to stop the car?
What is the coefficient of kinetic friction between tires and road?
vf^2=vi^2+2ad solve for a
work=KE of car initially
or work=force*distance=ma*distance
force=mu(mg)=ma
mu=a/g
To determine the car's acceleration while stopping, you can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity = 0 m/s (since the car comes to a halt)
u = initial velocity = 20 m/s (given)
a = acceleration (to be determined)
s = displacement = 64 m (given)
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Substituting the given values, we get:
a = (0^2 - 20^2) / (2 * 64)
a = (-400) / 128
a = -3.125 m/s^2
Therefore, the car's acceleration while stopping is -3.125 m/s^2 (negative sign indicates deceleration).
To calculate the work done by friction to stop the car, we can use the work-energy principle. The work done is equal to the change in kinetic energy of the car:
Work = ΔKE
Work = 1/2 * m * (v^2 - u^2)
Substituting the given values, we have:
Work = 1/2 * 1300 kg * (0^2 - 20^2)
Work = 1/2 * 1300 kg * (-400)
Work = -1/2 * 1300 kg * 400
Work = -260,000 joules
Therefore, the work done by friction to stop the car is -260,000 joules (negative sign indicates work against the direction of motion).
To find the coefficient of kinetic friction between the tires and the road, we can use the equation:
Force of friction = coefficient of friction * normal force
Since the car is skidding, the frictional force opposes the motion. It can be calculated using the equation:
Force of friction = mass * acceleration
Substituting the given values, we have:
mass * acceleration = coefficient of friction * normal force
Since the car is stopping, the acceleration is the deceleration we previously calculated: -3.125 m/s^2.
Therefore:
1300 kg * (-3.125 m/s^2) = coefficient of friction * normal force
Simplifying, we have:
coefficient of friction = (1300 kg * -3.125 m/s^2) / normal force
Unfortunately, we don't have the normal force information, so we cannot determine the coefficient of kinetic friction between the tires and the road without additional data.